Core Proxy Definition Ξ (t) = (1 / (ρ₀ V) ) ∫V ρ (r, t) − ρᵣef (r) w (r) dV Threshold Condition Ξcrit ≈ 10^ (-3) Instability Criterion Ξ (t) > Ξcrit ⇒ Dipole Instability Coherence Mapping k (t) = 1 / (1 + expβ (Ξ (t − τ) − Ξcrit) ) Dipole Moment M (t) = M₀ k (t) + ε (t) Mean-Field Coupling ∂B/∂t = ∇ × (α (Ξ) B) + η ∇² B α (Ξ) = α₀ (1 − Ξ / Ξcrit) Magnetic Reynolds Number Rₘ = U L / η Minimal Dynamical Model dΞ/dt = S (t) − γ Ξ dκ/dt = −λ κ − K_∞ (Ξ) K_∞ (Ξ) = 1 / (1 + expβ (Ξ − Ξcrit) )
Sadegh Sepehri (Thu,) studied this question.
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